Giovanni Trapattoni will look at the World Cup qualifying Group Eight table and smile. Results are the only thing that matter to the archly pragmatic Republic of Ireland manager and he simply does not care how he gets them. This vital victory, however, stretched the boundaries of credibility.

The spirited second-half efforts of his players were threatening to run aground when the tie became a freakish tale of two shoulders, one belonging to a Georgia defender and the other to the Ireland captain Robbie Keane.

With the angst of the Dublin crowd rising and their team trailing and struggling to prise apart stubborn, if tiring, opposition, Trapattoni's side were handed a scarcely believable penalty. Kevin Doyle smuggled the ball through towards Keane, who was flagged in an offside position, but before it reached him, it brushed Ucha Lobjanidze on the top of the shoulder. To the fury of the visiting team and the general bemusement of even the home crowd, the Finnish referee Jouni Hyytia pointed to the spot. A grateful Keane nervelessly converted the kick.

That was only the beginning. Shortly afterwards, Aiden McGeady swung over a corner and Keane, wrestling free of defensive shackles, stooped to squeeze a scruffy header, which came off his shoulder, past the goalkeeper Giorgi Lomaia and over the line. He and the rest of Croke Park descended into delirium.

"I don't know whether the penalty cost us the three points but for sure, it cost us one point, minimum," said a dignified and remarkably sanguine Hector Cuper, the Georgia manager. "The penalty penalised us very much. The situation was strange and vague, nobody understood the reason. The players are all very angry. We did not deserve to lose."

Trapattoni took issue with Cuper's last assertion, although he was forced to skate over the unfairness of the penalty award. "I am in football for 40 years and do you know how many penalties like this there are in every country?" he asked. "We had the luck in this situation but every Sunday in every country there are many situations like this. I think over the 90 minutes we deserved to win."

Keane had claimed beforehand that Ireland had a wonderful chance to win the group and in front of the Italy manager, Marcello Lippi, Ireland fashioned the victory that lifted them up alongside the world champions at the top of the table. They play Bulgaria next at home and immediately after that is the trip to Italy. They will approach the double header in good heart but the mood might have been different.

Ireland conceded a dreadful goal after 45 seconds, when Stephen Kelly hesitated and allowed Alexander Iashvili to steal in and beat Shay Given. Keith Andrews had a deflected shot ruled out for an offside flag against Doyle while Keane headed the clearest first-half chance at Lomaia.

The Georgian league is in its winter break and Cuper's fears that his players might lack stamina were realised. Even so, the game might have swung in their favour just before the hour when Levan Kobiashvili's deflected shot bounced off the post. Iashvili rolled the rebound into the net but was pulled back for offside.

With McGeady transformed, Ireland stepped up the intensity but they struggled to chisel out any clear-cut chances. Part of the frustration was that they did not work Lomaia thoroughly but enter Hyytia and everything changed. Optimism is now soaring and if Ireland's luck holds like this, they will be on the plane to South Africa next summer. Trapattoni will take that however it comes.